Given a matrix of 1s and 0s, is there a subset of the rows such that there is one and only one 1 in each column?

It turns out a lot of interesting problems can be encoded in such a way that the 1-cover algorithm can be used to solve them (For example, counting the number of possible solutions to a Sudoku puzzle). Knuth talks in general about exact-cover problems (placing dominoes on a chessboard, the N-queens problem, etc.), and how each of these are specializations of the 1-cover problem, and so can be solved by this algorithm.